Extended Data Figure 6. Vector-based Navigation Schema.
(Left) The hippocampus represents a goal-direction vector pointing from the animal to the goal (A) which decreases as the animal is farther from the goal (Right). The navigation system computes the projection of each choice platform vector (B, C) onto the goal direction vector (inner product, Bgd, Cgd) and selects the larger of the two. This choice is easier with increased angle between choices (β) and consequent increased difference in the magnitudes of their projection vectors. The projection vector of the preferred platform, Bgd, is the output of the system which competes with other potential solutions to the problem e.g. choose the left-most or North-most platform.